<h2>DESCRIPTION</h2>

<em>v.net.visibility</em> computes the visibility graph of a vector
map containing lines, areas (boundaries) and points. The visibility
graph is the graph where the nodes are the end point of the lines,
boundaries or simply points. There is an edge between two nodes if they
are 'visible' to each other. Two nodes are visibible if there are no segments
in between of them, i.e. the edge does not intersect any line or boundary
in the vector map. This is useful to compute the shortest path in a
vector map from any two points. To do this, first you need to compute
the visibility graph and from that to compute the shortest path using
<em><a href="v.net.path.html">v.net.path</a></em>
or <em><a href="d.path.html">d.path</a></em>.

<p>
<b>IMPORTANT: the algorithm doesn't work well with intersecting lines
(that includes overlapping)</b>

<h2>NOTES</h2>

If you compute a shortest path after computing the visibility graph
you will notice that this path might go through a vertex of a line. If
this is not what you wanted you might need to process the map
in <em><a href="v.buffer.html">v.buffer</a></em>, initially with a
small value. Example:

<div class="code"><pre>
v.buffer input=map output=bufferedmap buffer=1 type=point,line,area,boundary
</pre></div>

<p>
The first argument is the input map. It supports lines, boundaries 
(so, areas) and points. For the algorithm  was written to work with lines
and boundaries not intersecting each other (that includes overlapping).
<br>
The resulting map containing the visibility graph is given in the output map.
<p>
If you need to add additional points to compute a shortest path 
between them afterwards you can use the <b>coordinates</b> parameter, e.g.:
<div class="code"><pre>
coordinates=25556200,6686400,25556400,6686600
</pre></div>
where 25556200,6686400 are the coordinate of the first point and 
25556400,6686600 are the coordinates of the second point. Of course 
you can give as many points as you need. They will be added to the 
visibility graph and edges from them will be computed. You can 
always add those points after computing the visibility graph. Simply 
use the <b>visibility</b> parameter. The input will be the original 
vector map, the vis will be the computed visibility graph and the 
output the new visibility graph which will be the vis + the new 
points given with coordinate (edges will be computed as well).
<div class="code"><pre>
v.net.visibility input=map visibility=vis_map output=new_vis_map \
      coordinates=25556200,6686400,25556400,6686600
</pre></div>

<h2>EXAMPLES</h2>

<h3>Example 1</h3>

<!-- still overly complex result, some simple geometric were better -->
A simple example (North Carolina sample data) showing how to use the module:
<div class="code"><pre>
v.extract input=zipcodes_wake output=areas_7_11_25 cats=7,11,25
g.region vector=zipcodes_wake
d.mon wx0
d.vect areas_7_11_25
v.net.visibility input=areas_7_11_25 output=graph
d.vect graph
d.vect areas_7_11_25 color=red type=boundary
</pre></div>

<h3>Example 2</h3>d.er  
An example on how to use <em><a href="v.buffer.html">v.buffer</a></em>
along with the module:
<div class="code"><pre>
v.buffer input=lines output=buffered_lines buffer=1
v.net.visibility input=buffered_lines output=graph
d.vect graph
d.vect lines col=red
</pre></div>


<h3>Example 3</h3>
An example on how to use the coordinate parameter. This will compute the
visibility graph of the vector map lines with the point 2555678,6686343:
<div class="code"><pre>
v.net.visibility input=lines output=graph coordinates=2555678,6686343
d.vect graph
d.vect lines col=red
</pre></div>

<h3>Example 4</h3>
<!-- does not quite ork yet? -->
An example (North Carolina sample data) on how to use the coordinate
parameter with the vis parameter.
Here the vector map graph is computed then a new visibility graph is computed
from it with the point 669547.97,208348.20 extra:
<div class="code"><pre>
v.extract input=zipcodes_wake output=areas_7_11_25 cats=7,11,25
g.region vector=zipcodes_wake
d.mon wx0
d.vect areas_7_11_25
v.net.visibility input=areas_7_11_25 output=graph
v.net.visibility input=areas_7_11_25 visibility=graph output=new_graph \
      coordinates=669547.97,208348.20
d.erase
d.vect areas_7_11_25
echo "symbol basic/star 20 669547.97 208348.20 black red" | d.graph -m
d.vect new_graph
d.vect areas_7_11_25 color=red type=boundary
</pre></div>


<h3>Example 5</h3>
An example for connections of points (Spearfish):
<div class="code"><pre>
v.net.visibility input=archsites output=graph
g.region vector=archsites
d.mon wx0
d.vect graph
d.vect archsites col=red
</pre></div>

<h3>Example 6</h3>

Here is an example with artificial data.

<p>
<img src="v_net_visibility.png">

<p>
Load data using here document syntax (Bash and unix-like commands lines only):

<div class="code"><pre>
v.in.ascii input=- output=simple format=standard &lt;&lt;EOF
VERTI:
B  6
 82.19908257  75.21788991
 81.67889908  71.40321101
 83.58623853  71.72522936
 84.3293578   75.21788991
 82.24862385  76.06009174
 82.19908257  75.21788991
C  1 1
 82.88897401  73.66318782
 1     1
C  1 1
 90.72645705  75.61248675
 1     2
C  1 1
 89.37944702  69.51012912
 1     3
C  1 1
 81.60108979  67.78669725
 1     4
B  5
 89.92752294  73.95458716
 92.37981651  75.11880734
 91.56238532  77.29862385
 88.96146789  75.88669725
 89.92752294  73.95458716
B  10
 88.54036697  70.70963303
 87.92192518  70.04087417
 87.89633028  69.00045872
 88.66460807  68.13372867
 90.15108904  68.23290821
 90.9426344   68.97588202
 90.86880734  70.11513761
 90.00144697  70.78336312
 89.06055046  70.95733945
 88.54036697  70.70963303
B  9
 78.73119266  71.35366972
 80.76238532  68.90137615
 84.20550459  66.91972477
 89.87798165  65.35917431
 83.23494031  66.27685175
 80.34278748  68.00837238
 78.38484005  71.40292009
 78.40917431  72.27018349
 78.73119266  71.35366972
EOF
</pre></div>

Compute the graph:

<div class="code"><pre>
v.net.visibility input=simple output=graph
</pre></div>

<h2>KNOWN ISSUES</h2>
In some cases when 3 points or nodes are collinear, some wrong edges 
are added. This happens only really rarly and shouldn't be a big 
problem. When two points have the exact same x coordinate and are 
visible, some wrong edges are added.

<h2>SEE ALSO</h2>

<em>
<a href="d.path.html">d.path</a>,
<a href="v.net.html">v.net</a>,
<a href="v.net.alloc.html">v.net.alloc</a>,
<a href="v.net.iso.html">v.net.iso</a>,
<a href="v.net.salesman.html">v.net.salesman</a>,
<a href="v.net.steiner.html">v.net.steiner</a>,
<a href="v.to.db.html">v.to.db</a>
</em>

<h2>AUTHOR</h2>
Maximilian Maldacker<br>
Mentor: Wolf Bergenheim

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